Returns the pseudo-Vandermonde matrix of degrees deg and sample
points (x, y, z). If l, m, n are the given degrees in x, y, z,
then The pseudo-Vandermonde matrix is defined by

where 0 <= i <= l, 0 <= j <= m, and 0 <= j <= n. The leading
indices of V index the points (x, y, z) and the last index encodes
the powers of x, y, and z.

If V=polyvander3d(x,y,z,[xdeg,ydeg,zdeg]), then the columns
of V correspond to the elements of a 3-D coefficient array c of
shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order

and np.dot(V,c.flat) and polyval3d(x,y,z,c) will be the
same up to roundoff. This equivalence is useful both for least squares
fitting and for the evaluation of a large number of 3-D polynomials
of the same degrees and sample points.

Parameters:

x, y, z : array_like

Arrays of point coordinates, all of the same shape. The dtypes will
be converted to either float64 or complex128 depending on whether
any of the elements are complex. Scalars are converted to 1-D
arrays.

deg : list of ints

List of maximum degrees of the form [x_deg, y_deg, z_deg].

Returns:

vander3d : ndarray

The shape of the returned matrix is x.shape+(order,), where
. The dtype will
be the same as the converted x, y, and z.